Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
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In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.Abstract:
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, γ. When γ is small, Bogoliubov’s perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of γ and show that it is analytic for all γ, except γ=0. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum—not one as is ordinarily supposed.read more
Citations
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Journal ArticleDOI
Spatial entanglement entropy in the ground state of the Lieb-Liniger model
TL;DR: In this paper, the entanglement between two spatial subregions in the Lieb-Liniger model of bosons in one spatial dimension interacting via a contact interaction was considered.
Journal ArticleDOI
Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas
TL;DR: In this paper, an impurity in a semi-infinite one-dimensional system of weakly-interacting bosons is considered and the interaction potential for the impurity due to the end of the system, i.e., the wall.
Journal ArticleDOI
Low-density, one-dimensional quantum gases in the presence of a localized attractive potential
TL;DR: In this paper, the authors investigated low-density, quantum-degenerate gases in the presence of a localized attractive potential in the center of a one-dimensional harmonic trap.
Journal ArticleDOI
Spectrum of Elementary Excitations in Galilean-Invariant Integrable Models.
TL;DR: It is shown that the spectrum at arbitrary momentum is fully determined by the properties of the ground state, and general exact relations for the coefficients of several terms in the expansion of the excitation energy at low momenta and arbitrary interaction are found.
Book ChapterDOI
Quantum Inverse Scattering Method
TL;DR: The quantum inverse scattering method as mentioned in this paper is one of the most important discoveries in modern mathematical physics and it is a unique method whereby the initial value problem of a nonlinear evolution equation is solved.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Journal ArticleDOI
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
TL;DR: In this article, a rigorous one-one correspondence between one-dimensional systems of bosons and spinless fermions is established, subject only to the restriction that the interaction has an impenetrable core.
Journal ArticleDOI
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
TL;DR: In this paper, the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum was carried out and it was shown that the elementary excitations are most naturally thought of as a double spectrum, not a single one.
Journal ArticleDOI
Linear antiferromagnetic chain with anisotropic coupling
TL;DR: In this article, the exact solution for a linear chain of spin atoms coupled together by the anisotropic Hamiltonian was given for the antiferromagnetic ground state and comparison was made with a variational method.
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